Decentralized Swarm Control via SO(3) Embeddings for 3D Trajectories

2025-11-13

AI Summary

This paper addresses the challenge of 3D cooperative formation control for multi-agent systems under minimal information sharing. We propose a distributed geometric control framework relying solely on relative position measurements. The method constructs periodic 3D trajectories via SO(3) Lie group embedding—eliminating conventional velocity feedback—and designs a phase-synchronization controller to ensure uniform formation spacing, supported by formal stability analysis. Key contributions include: (1) an extended quaternion representation enabling robust trajectory generation on SO(3); (2) the first distributed phase-control law utilizing pure position feedback; and (3) experimental validation—both in simulation and on physical quadrotors—demonstrating strong robustness against low-level dynamic uncertainties and external disturbances. Results show that the approach achieves high-quality, self-organized, periodic 3D formations efficiently and reliably.

Technology Category

• Multiagent Systems: Coordination and Collaboration
• Intelligent Robots: State Estimation
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Location- and context-aware Web and WoT applications and services
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

This paper presents a novel decentralized approach for achieving emergent behavior in multi-agent systems with minimal information sharing. Based on prior work in simple orbits, our method produces a broad class of stable, periodic trajectories by stabilizing the system around a Lie group-based geometric embedding. Employing the Lie group SO(3), we generate a wider range of periodic curves than existing quaternion-based methods. Furthermore, we exploit SO(3) properties to eliminate the need for velocity inputs, allowing agents to receive only position inputs. We also propose a novel phase controller that ensures uniform agent separation, along with a formal stability proof. Validation through simulations and experiments showcases the method's adaptability to complex low-level dynamics and disturbances.

Problem

• Achieving emergent swarm behavior with minimal information sharing
• Generating stable periodic trajectories using SO(3) geometric embeddings
• Ensuring uniform agent separation without velocity inputs

Innovation

• Decentralized swarm control using SO(3) embeddings
• Generates periodic trajectories without velocity inputs
• Novel phase controller ensures uniform agent separation